Okay, we are tasked with adding 8741 and 6623. Let's begin!

Step 1: We'll start by adding the digits 1 & 3 in column 1 and get 4.

Step 2: We'll start by adding the digits 4 & 2 in column 2 and get 6.

Step 3: We'll start by adding the digits 7 & 6 in column 3 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 8 & 6 in column 4 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

So, 8741 + 6623 = 15364.

